Property 5: Refraction experiment ? particle (photon)? wave (E&M) ?
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Transcript of Property 5: Refraction experiment ? particle (photon)? wave (E&M) ?
Property 5: Refraction
experiment ?
particle (photon)?
wave (E&M) ?
Property 5: Refraction
• experiment: objects in water seem closer than they really are when viewed from air
air
water
real object
apparentlocation
eye
Property 5: Refraction
• particle (photon) ?
water
air
surface
incident ray
refracted ray
Property 5: Refraction
• particle (photon) ?
water
air
surface
incident ray
refracted ray
vxair
vyair
vxwater
vywater
vxair = vxwater
vyair < vywater
thereforevi < vr
Property 5: Refraction
• wave (E&M) ?
surface
air
water
incident wave
refracted wave
normal line
normal line
surface
Property 5: Refraction
• wave (E&M) ?
surface
air
water
incident wave
refracted wave
crest of wave
crest of preceding wave
x
air
water
normal line
crest of following wave
air
Property 5: Refraction
• particle (photon) theory: vwater > vair
• wave (E&M) theory: vwater < vair
• experiment ?
Property 5: Refraction
• particle (photon) theory: vwater > vair
• wave (E&M) theory: vwater < vair
• experiment: vwater < vair
wave theory works!
particle theory fails!
Properties 1, 2 & 5
Speed, Color and Refraction• Speed of light changes in different materials
• Speed is related to frequency and wavelength: v = f
• If speed changes, does wavelength change, frequency change, or BOTH?
Properties 1, 2 & 5• Speed, Color and Refraction• Speed of light changes in different materials• Speed is related to frequency and
wavelength: v = f• What changes with speed?
– Frequency remains constant regardless of speed
– Wavelength changes with speed
Refraction and Thin Lenses
Can use refraction to try to control rays of light to go where we want them to go.
Let’s see if we can FOCUS light.
Refraction and Thin Lenses
What kind of shape do we need to focus light from a point source to a point?
lens with some shape for front & back
screen
pointsourceof light
s = object distances’ = image distance
Refraction and Thin Lenses
Let’s try a simple (easy to make) shape: SPHERICAL.
Play with the lens that is handed outDoes it act like a magnifying glass?
Refraction and Thin Lenses
Let’s try a simple (easy to make) shape: SPHERICAL.
Play with the lens that is handed outDoes it act like a magnifying glass?
Does it focus light from the night light?
Refraction and Thin Lenses
Let’s try a simple (easy to make) shape: SPHERICAL
Play with the lens that is handed outDoes it act like a magnifying glass?
Does it focus light from the night light?
Does the image distance depend on the shape of the lens? (trade with your neighbor to get a different shaped lens)
Refraction and Thin Lenses
Spherical shape is specified by a radius.
The smaller the sphere (smaller the radius),
the more curved is the surface!
RR
R1
R2
Refraction and the Lens-users Eq.
1
f =
1
s +
1
s'
f f
ss’
s > 0 AND s > f
s’ > 0 AND s’ > f
f > 0
Example: f = 10 cm; s = 20 cm; s’ = 20 cm: 1/20 + 1/20 = 1/10
Refraction and the Lens-users Eq.
1
f =
1
s +
1
s'
f f
ss’
as s gets bigger,s’ gets smaller
Example: f = 10 cm; s = 40 cm; s’ = 13.3 cm: 1/40 + 1/13.3 = 1/10
Refraction and the Lens-users Eq.
1
f =
1
s +
1
s'
f f
s s’
as s approaches infinitys’ approaches f
Example: f = 10 cm; s = 100 cm; s’ = 11.1 cm: 1/100 + 1/11.1 = 1/10
Refraction and the Lens-users Eq.
1
f =
1
s +
1
s'
f f
ss’
s > 0 AND s > f
s’ > 0 AND s’ > f
f > 0
Example: f = 10 cm; s = 20 cm; s’ = 20 cm: 1/20 + 1/20 = 1/10
Refraction and the Lens-users Eq.
1
f =
1
s +
1
s'
f f
s
s’
as s gets smaller,s’ gets larger
Example: f = 10 cm; s = 13.3 cm; s’ = 40 cm: 1/13.3 + 1/40 = 1/10
Refraction and the Lens-users Eq.
1
f =
1
s +
1
s'
f f
ss’
as s approaches f,s’ approaches infinity
Example: f = 10 cm; s = 11.1 cm; s’ = 100 cm: 1/11.1 + 1/100 = 1/10
Refraction and the Lens-users Eq.
Before we see what happens when s gets smaller than f, let’s use what we already know to see how the lens will work.
Refraction and the Lens-users Eq.
f f
– Any ray that goes through the focal point on its way to the lens, will come out parallel to the optical axis. (ray 1)
ray 1
Refraction and the Lens-users Eq.
f f
– Any ray that goes through the focal point on its way from the lens, must go into the lens parallel to the optical axis. (ray 2)
ray 1
ray 2
Refraction and the Lens-users Eq.
f f
– Any ray that goes through the center of the lens must go essentially undeflected. (ray 3)
ray 1
ray 2
ray 3
object
image
Refraction and the Lens-users Eq.
f f
– Note that a real image is formed.
– Note that the image is up-side-down.
ray 1
ray 2
ray 3
object
image
Refraction and the Lens-users Eq.
f f
– By looking at ray 3 alone, we can see
by similar triangles that M = h’/h = -s’/s.
ray 3
object
image
s
h s’
h’<0
note h’ is up-side-downand so is <0
Example: f = 10 cm; s = 40 cm; s’ = 13.3 cm:
M = -13.3/40 = -0.33 X
Refraction and the Lens-users Eq.
f f
This is the situation when the lens is used
in a camera or a projector. Image is REAL.
ray 1
ray 2
ray 3
object
image
Refraction and the Lens-users Eq.
f f
What happens when the object distance, s, changes?
ray 1
ray 2
ray 3
object
image
Refraction and the Lens-users Eq.
f f
Notice that as s gets bigger, s’ gets closer to f and |h’| gets smaller.
ray 1
ray 2
ray 3
object
image
Example: f = 10 cm; s = 100 cm; s’ = 11.1 cm:
M = -11.1/100 = -0.11 X
FocusingTo focus a camera, we need to change s’ as s
changes. To focus a projector, we need to change s as s’ changes. We do this by screwing the lens closer or further from the film or slide.
But what about the eye? How do we focus on objects that are close and then further away with our eyes? Do we screw our eyes in and out like the lens on a camera or projector?
Focusing
But what about the eye? How do we focus on objects that are close and then further away with our eyes? Do we screw our eyes in and out like the lens on a camera or projector? - NO, instead our eyes CHANGE SHAPE and hence change f as s changes, keeping s’ the same!
Refraction and the Lens-users Eq.
f f
Let’s now look at the situation where
s < f (but s is still positive):
s
Refraction and the Lens-users Eq.
f f
We can still use our three rays. Ray one goes
through the focal point on the left side.
s
ray 1
Refraction and the Lens-users Eq.
f f
Ray two goes through the focal point on the
right side (and parallel to the axis on the left).
s
ray 1
ray 2
Refraction and the Lens-users Eq.
f f
Ray three goes through the center of the lens
essentially undeflected.
s
ray 1
ray 2
ray 3
s’
h’
Refraction and the Lens-users Eq.
f f
Notice that: s’ is on the “wrong” side, which
means that s’ < 0 , and that |s’| > |s| so f > 0.
s
ray 1
ray 2
ray 3
s’
h’
Example: f = 10 cm; s = 7.14 cm; s’ = -25 cm: 1/7.14 + 1/(-25) = 1/10
Refraction and the Lens-users Eq.
f f
Notice that: h’ right-side-up and so h’ > 0.,
M = h’/h = -s’/s . M > 0 (s’ < 0 but -s’ > 0).
s
ray 3
s’
h’
Example: f = 10 cm; s = 7.14 cm; s’ = -25 cm: M = - (-25)/ 7.14 = 3.5 X
Refraction and the Lens-users Eq.
f f
This is the situation when the lens is used
as a magnifying glass! Image is VIRTUAL.
s
ray 1
ray 2
ray 3
s’
h’
Refraction and the Lens-users Eq.
The same lens can be used as:
• a camera lens: s >> f, s > s’,
M < 0, |M| < 1
• a projector lens: s > f, s’ > s,
M < 0, |M| > 1
• a magnifying glass: s < f, s’ < 0,
M > 0, M > 1
Refraction and the Lens-users Eq.
Notes on using a lens as a magnifying glass:
• hold lens very near your eye
• want IMAGE at best viewing distance
which has the nominal value of 25 cm
so that s’ = -25 cm.
Refraction and the Lens-users Eq.
Are there any limits to the magnifying power
we can get from a magnifying glass?
Refraction and the Lens-users Eq.
• Magnifying glass has limits due to size
• As we will see in a little bit, magnifying
glass has limits due to resolving ability
• NEED MICROSCOPE (two lens system) for near and small things; need TELESCOPE (two lens system) for far away things.
Telescope Basics
Light from far away is almost parallel.
objectivelens eyepiece
fo
fe
Telescope Basics:Get More Light
The telescope collects and concentrates light.
objectivelens eyepiece
fo
fe
Telescope Basics
Light coming in at an angle, in is magnified to out .
objectivelens eyepiece
fofe
x
Magnification
in = x/fo, out = x/fe; M = out/in = fo/fe
objectivelens eyepiece
fofe
x
Limits on Resolution
telescopes– magnification: M = out/in = fo /fe – light gathering: Amt D2
– resolution: 1.22 = D sin(limit) so
in = limit and out = 5 arc minutes
so limit 1/D implies Museful = 60/in * D where D is in inches– surface must be smooth on order of
Limits on Resolution:calculation
Mmax useful = out/in = eye/limit
= 5 arc min / (1.22 * / D) radians
= (5/60)*(/180) / (1.22 * 5.5 x 10-7 m / D)
= (2167 / m) * D * (1 m / 100 cm) * (2.54 cm / 1 in)
= (55 / in) * D
Example
What diameter telescope would you need to read letters the size of license plate numbers from a spy satellite?
Example
• need to resolve an “x” size of about 1 cm
• “s” is on order of 100 miles or 150 km
• limit then must be (in radians)
= 1 cm / 150 km = 7 x 10-8
• limit = 1.22 x 5.5 x 10-7 m / D = 7 x 10-8
so D = 10 m (Hubble has a 2.4 m diameter)
Limits on Resolution: further examples
• other types of light– x-ray diffraction (use atoms as slits)– IR– radio & microwave
• surface must be smooth on order of
Review of Telescope Properties
1. Magnification: M = fo/fe depends on the focal lengths of the two lenses.
2. Light gathering ability: depends on area of objective lens, so depends on diameter of objective lens squared (D2).
3. Resolution ability: depends on diameter of objective lens: Max magnification = 60 power/in * D.
Types of Telescopes
The type of telescope we have looked at so far, and the type we have or will have made in the lab is called a refracting telescope, since it uses the refraction of light going from air to glass and back to air. This is the type used by Galileo.
There is a second type of telescope invented by Newton. It is called the reflecting telescope since it uses a curved mirror instead of a curved lens for the objective. There are three main sub-types of reflectors that we’ll consider: Prime focus, Newtonian, and Cassegranian.
Refracting Telescope
Two lenses (as we had in the lab)
objectivelens eyepiece
fo
fe
Reflecting Telescope
Light from far away mirror
focuses light
problem: how do we get to focused light without blocking incoming light?
Reflecting TelescopePrime Focus
Light from far away mirror focues light
Solution #1: If mirror is big enough (say 100 to 200 inches in diameter), we can sit right in the middle and we won’t block much light - this is called the prime focus.
eyepiece
Reflecting TelescopeNewtonian Focus
Light from far away primary
mirror focuses
light
Solution #2: Use secondary mirror to reflect light out the side of the telescope- this is called the Newtonian focus.
mirror
eyepiece
Reflecting TelescopeCassegranian Focus
Light from far away primary mirror
focuses light
eyepiece
Solution #3: Use secondary mirror to reflect light out the back of the telescope- this is called the Cassegranian focus.
mirror